Fulham, whose last win came over a month ago against Aston Villa at Craven Cottage, fully deserved their victory despite failing to produce too many clear-cut opportunities.
Everton, who have now failed to win at Fulham since Alan Ball netted the winner in 1966, rarely looked like avoiding their first Premier League defeat of 2008 with David Moyes' side still looking hungover from their painful exit from the UEFA Cup.
In a dire first half, neither team managed to adapt to the horrendous conditions with Fulham failing to muster a single effort on target.
Everton faired little better, although Ayegbeni Yakubu did force Kasey Keller into a comfortable save after bulldozing his way through the home defence.
The visitors, who saw Andrew Johnson substituted after just 14 minutes, looked the more accomplished of the two sides, but with the swirling wind making the game hazardous for both sets of players, there was little quality on display.
Eddie Johnson's searing pace was a constant menace, although the American's insistence at taking the ball away from goal rather than to it remained something of a mystery throughout.
It was Everton that continued the most likely to open the scoring and Phil Neville should have done better after being played through by Yakubu, but the former Manchester United man saw his effort brilliantly blocked by Paul Konchesky.
And the visitors were made to rue that miss as Fulham took the lead almost immediately with their first effort on target in the entire game.
Davies escaped down the left and the Wales international's cross was inadvertently flicked on by Joseph Yobo, allowing McBride to steal in between the two central defenders and head powerfully past Tim Howard.
The goal sparked wild celebrations inside Craven Cottage, but they should have been brought to a shuddering halt just three minutes later as Yobo missed a glorious opportunity to restore parity by sending a free header wide from a mere six yards.
With Everton pushing forward in search of an equaliser, the game began to open up with the visitors leaving gaps in their defence.
And Moyes' side should have been punished for their approach after a sloppy clearance from Yobo fell straight into the path of Eddie Johnson, only for the striker to fire aimlessly over the bar with the goal gaping.
Their confidence bolstered by the goal, Fulham broke free of the shackles that have left them bound in recent weeks and Davies, another former Everton man, really should have put the game beyond doubt with eight minutes to play.
Jimmy Bullard's exquisite through ball released Davies, but the midfielder could only fire wide of the post when it appeared easier to score.
Fulham continued to push forward in the later stages with Eddie Johnson sending yet another effort high over Howard's crossbar, but that miss proved insignificant as the home side held on for a much-needed victory.